Informatica

There exist various types of similarity measures for intuitionistic fuzzy sets in the literature. However, in many studies the interactions among the elements are ignored in the construction of the similarity measure. This paper presents a cosine similarity measure for intuitionistic fuzzy sets by using a Choquet integral model in which the interactions between elements are considered. The proposed similarity measure is applied to some pattern recognition problems and the results are compared with some existing results to demonstrate the effectiveness of this new similarity measure.

The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in $[0\mathrm{,}1]$. Considering the order relationship between hesitant fuzzy 2-tuple linguistic term sets, measures of expected value and variance are defined. Meanwhile, several induced generalized hesitant fuzzy 2-tuple linguistic aggregation operators are defined, by which the comprehensive attribute values of alternatives can be obtained. Then, models for the optimal weight vector on a decision maker set, on an attribute set and on their ordered sets are constructed, respectively. Furthermore, an approach to multi-granularity group decision making with hesitant fuzzy linguistic information is developed. Finally, an example is selected to illustrate the feasibility and practicality of the proposed procedure.

In this paper, we focus on group decision making problems with uncertain preference ordinals, in which the weight information of decision makers is completely unknown or partly unknown. First of all, the consistency and deviation measures between two uncertain preference ordinals are defined. Based on the two measures, a multi-objective optimization model which aims to maximize the deviation of each decision maker’s judgements and the consistency among different decision makers’ judgements is established to obtain the weights of decision makers. The compromise solution method, i.e. the VIKOR method is then extended to derive the compromise solution of alternatives for group decision making problems with uncertain preference ordinals. Finally, three examples are utilized to illustrate the feasibility and effectiveness of the proposed approach.

With respect to multi-attribute decision making under uncertain linguistic environment, a new interval-valued 2-tuple linguistic representation model is introduced. To deal with the situation where the elements in a set are interdependent, several generalized interval-valued 2-tuple linguistic correlated aggregation operators are defined. It is worth pointing out that some interval-valued 2-tuple linguistic operators based on additive measures are special cases of our operators. Meanwhile, several special cases and desirable properties are discussed. Furthermore, models based on the correlation coefficient are constructed, by which the optimal weight vector can be obtained. Moreover, an approach to multi-attribute group decision making with uncertain linguistic information is developed. Finally, an example is selected to show the effectivity and feasibility of the developed procedure.

We present a new aggregation operator called the generalized ordered weighted proportional averaging (GOWPA) operator based on an optimal model with penalty function, which extends the ordered weighted geometric averaging (OWGA) operator. We investigate some properties and different families of the GOWPA operator. We also generalize the GOWPA operator. The key advantage of the GOWPA operator is that it is an aggregation operator with theoretic basis on aggregation, which focuses on its structure and importance of arguments. Moreover, we propose an orness measure of the GOWPA operator and indicate some properties of this orness measure. Furthermore, we introduce the generalized least squares method (GLSM) to determine the GOWPA operator weights based on its orness measure. Finally, we present a numerical example to illustrate the new approach in an investment selection decision making problem.